Program d04bafe

!     D04BAF Example Program Text
!     Mark 30.1 Release. NAG Copyright 2024.

!     .. Use Statements ..
      Use nag_library, Only: d04baf, d04bbf, nag_wp, s14aef
!     .. Implicit None Statement ..
      Implicit None
!     .. Parameters ..
      Real (Kind=nag_wp), Parameter    :: x_0 = 0.05_nag_wp
      Integer, Parameter               :: nout = 6, n_der_comp = 3,            &
                                          n_display = 3, n_hbase = 4,          &
                                          zeroth = 0
!     .. Local Scalars ..
      Real (Kind=nag_wp)               :: hbase
      Integer                          :: ifail, j, k
!     .. Local Arrays ..
      Real (Kind=nag_wp)               :: actder(n_display), der(14),          &
                                          der_comp(n_hbase,n_der_comp,14),     &
                                          erest(14), fval(21), xval(21)
!     .. Executable Statements ..
      Write (nout,*) 'D04BAF Example Program Results'
      Write (nout,*)
      Write (nout,*) ' Find the derivatives of the polygamma (psi) function'
      Write (nout,*) ' using function values generated by S14AEF.'
      Write (nout,*)
      Write (nout,*) ' Demonstrate the effect of successively reducing HBASE.'
      Write (nout,*)
!     Select an initial separation distance HBASE.
      hbase = 0.0025_nag_wp

!     Compute the actual derivatives at target location x_0 using s14aef for
!     comparison.
      Do j = 1, n_display
        ifail = 0
        actder(j) = s14aef(x_0,j,ifail)
      End Do

!     Attempt N_HBASE approximations, reducing HBASE by factor 0.1 each time.
      Do j = 1, n_hbase

!       Generate the abscissa XVAL using D04BBF
        Call d04bbf(x_0,hbase,xval)

!       Calculate the corresponding objective function values.
        Do k = 1, 21
          ifail = 0
          fval(k) = s14aef(xval(k),zeroth,ifail)
        End Do

!       Call D04BAF to calculate the derivative estimates
        ifail = 0
        Call d04baf(xval,fval,der,erest,ifail)

!       Store results in DER_COMP
        der_comp(j,1,1:14) = hbase
        der_comp(j,2,1:14) = der(1:14)
        der_comp(j,3,1:14) = erest(1:14)

!       Decrease hbase for next loop
        hbase = hbase*0.1_nag_wp
      End Do

!     Display Results for first N_DISPLAY derivatives

      Do j = 1, n_display
        Write (nout,99999) j, actder(j)
        Write (nout,99998) j
        Write (nout,99997) j, j
        Do k = 1, n_hbase
          Write (nout,99996) der_comp(k,1,j), der_comp(k,2,j), der_comp(k,3,j)
        End Do
        Write (nout,*)
      End Do

99999 Format (1X,' Derivative (',I1,') calculated using S14AEF :',1X,Es11.4)
99998 Format (1X,' Derivative and error estimates for derivative (',I1,')')
99997 Format (10X,'hbase       DER(',I1,')     EREST(',I1,')')
99996 Format (1X,1P,E14.4,E13.4,E13.1)
    End Program d04bafe